Combinatorics of Permutations

by Miklos Bona

Overview

A CHOICE "Outstanding Academic Title," the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, third edition continues to clearly show the usefulness of this subject for both students and researchers.

The research in combinatorics of permutations has advanced rapidly since this book was published in a first edition. Now the third edition offers not only updated results, it remains the leading textbook for a course on the topic.

Coverage is mostly enumerative, but there are algebraic, analytic, and topological parts as well, and applications.

Since the publication of the second edition, there is tremendous progress in pattern avoidance (Chapters 4 and 5). There is also significant progress in the analytic combinatorics of permutations, which will be incorporated.

•A completely new technique from extremal combinatorics disproved a long-standing conjecture, and this is presented in Chapter 4.

•The area of universal permutations has undergone a lot of very recent progress, and that has been noticed outside the academic community as well. This also influenced the revision of Chapter 5.

•New results in stack sorting are added to Chapter 8.

•Chapter 9 applications to biology has been revised.

The author’s other works include Introduction to Enumerative and Analytic Combinatorics, second edition (CHOICE "Outstanding Academic Title") and Handbook of Enumerative Combinatorics, published by CRC Press. The author also serves as Series Editor for CRC’s Discrete Mathematics and Its Applications.

Product Details

ISBN-13:	9780367222581
Publisher:	CRC Press
Publication date:	05/10/2022
Series:	Discrete Mathematics and Its Applications
Edition description:	3rd ed.
Pages:	528
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Miklós Bóna received his Ph.D in mathematics from the Massachusetts Institute of Technology in 1997. Since 1999, he has taught at the University of Florida, where, in 2010, he was inducted into the Academy of Distinguished Teaching Scholars. Professor Bóna has mentored numerous graduate and undergraduate students. He is the author of four books and more than 65 research articles, mostly focusing on enumerative and analytic combinatorics. His book, Combinatorics of Permutations, won a 2006 Outstanding Title Award from Choice, the journal of the American Library Association. He is also an editor-in-chief for the Electronic Journal of Combinatorics, and for two book series at CRC Press.

Table of Contents

Foreward
Preface to the First Edition
Preface to the Second Edition
Preface to the Third Edition
Acknowledgements
Introduction: No Way around It.
1.In One Line and Close: Permutations as Linear Orders
2.In One Line and Anywhere: Permutations as Linear Orders- Inversions
3.In Many Circles: Permutations as Products of Cycles
4.In Any Way but This: Pattern Avoidance—the Basics
5.In This Way, but Nicely: Pattern Avoidance-Follow Up
6.Mean and Insensitive: Random Permutations
7.Permutations and the Rest: Algebraic Combinatorics of Permutations
8.Get Them All: Algorithms and Permutations
9.How Did We Get Here? Permutations as Genome Rearrangements
Do Not Look Just Yet: Solutions to Odd-Numbered Exercises
References
List of Frequently Used Notation
Index

Editorial Reviews

The extended new edition of Bóna’s textbook will continue to provide a wealth of information on the combinatorial facet of permutations, to both students and researchers in the subject.
— Martin Kiazar, in Mathematical Review Clippings

There is a new chapter nine, ‘devoted to sorting algorithms whose original motivation comes from molecular biology.’ Chapters 1, 3, 4, and 6 have been ‘significantly changed and expanded’ and all chapters have new exercises and problems, some of which reflect recent results. This is an excellent book on an important subject.
—Fernando Q. Gouvêa, MAA Reviews, December 2012 (This book is in the MAA's basic library list.)

How is the newcomer to this subject able to make sense of and sort out these bewildering possibilities? Until now it was necessary to consult a myriad of sources, from textbooks to journal articles, in order to grasp the whole picture. Now, however, Miklós Bóna has provided us with a comprehensive, engaging, and eminently readable introduction to all aspects of the combinatorics of permutations. The chapter on pattern avoidance is especially timely and gives the first systematic treatment of this fascinating and active area of research.
This book can be utilized at a variety of levels, from random samplings of the treasures therein to a comprehensive attempt to master all the material and solve all the exercises. In whatever direction the reader’s tastes lead, thorough enjoyment and appreciation of a beautiful area of combinatorics are certain to ensue.
—From the Foreword by Richard Stanley, MIT

Praise for the First Edition:
Winner of a 2006 CHOICE Outstanding Academic Title Award
One can easily imagine gems from this book forming the basis of a Martin Gardner-type column … the fascinating chapters here on pattern avoidance, particularly the formulation and proof of the Stanley-Wilf and Furedi-Hajnal conjectures, make this book essential … The author shows himself the master expositor, always efficient while never terse, ever the clairvoyant and generous anticipator of misreadings that might trip readers. Summing Up: Essential.
—CHOICE

Throughout the book, there are frequent references to the excellent bibliography of more than two hundred research articles and books. It is clear that the author finds his topic to be full of ‘serious fun.’ This enthusiasm is conveyed in the conversational and engaging style of the writing … This book was written to be used in a graduate-level topics course. For that purpose it is ideally suited … Experienced researchers in combinatorics will find the book useful as a guide to the literature on permutations. For graduate students with advanced interests in any field of combinatorics, the faculty who work with these students, or the libraries that support them, this book is an excellent choice.
—SIAM Review

This advanced-level textbook grew out of a graduate combinatorics topics class. It serves that role quite well. … Applications are nicely sprinkled throughout the text. … a very extensive list of references with 208 entries … will be attractive to researchers in the area. This excellent text would serve a graduate seminar very well, but could also be used by advanced undergraduates who already have a background in combinatorics.
—Herbert E. Kasube, MAA Reviews

The literature on permutations is as extensive as permutations are manifold … What was missing until now was a comprehensive, up-to-date treatment of all aspects of the combinatorics of permutations … This is the first book which gives a systematic introduction to this fascinating and active area of research … All the subjects are presented in a very pleasant way: developments are always well motivated, explanations are transparent and illustrated by numerous examples. At the end of each chapter the reader finds a list of exercises, with detailed solutions … [containing] references [that] … are excellent starting points for further research.
—Zentralblatt für Mathematik

We found the author’s explanations very clear, and there is an abundance of useful examples and helpful figures . . . There is a rich bibliography for those seeking more information or full proofs of cited results.
—R. Gregory Taylor, SIGACT News, October 2008

[This book] was written by the author with love and enthusiasm for the subject and is a pleasure to read. Undergraduate and graduate students in combinatorics as well as researchers will find in it many interesting results and inspiring questions.
—Mathematical Reviews, 2005

From the Publisher